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		<P class='majorTitle'>com.wis.math.alg.Decomposition Documentation</P>

        <P><B>Author:</B> <a href='mailto:wisolutions2002@shaw.ca?subject=wisASLibrary  Decomposition Class'>Richard Wright</a><BR>
		<B>Last Modified:</B> 01/13/05 13:32:53<HR class='big'>

		<P class='sectionTitle'>Summary</P>
		<P class='ToC'>com.wis.math.alg.Decomposition class:</P>
		<div class='methodsDiv'><a href='#classinfo'>- description</a></div>
<P class='ToC'>com.wis.math.alg.Decomposition Properties:</P><div class='methodsDiv'>
<a href='#$order'>- $order</a><br>
<a href='#$element'>- $element</a><br>
<a href='#$index'>- $index</a><br>
<a href='#$newtonIter'>- $newtonIter</a><br>
<a href='#$newtonMaxIter'>- $newtonMaxIter</a><br>
<a href='#$debug'>- $debug</a><br>
</div><br>
<P class='ToC'>com.wis.math.alg.Decomposition Methods:</P><div class='methodsDiv'>
<a href='# squareMatrixCreate'>-  squareMatrixCreate</a><br>
<a href='# symMatrixCreate'>-  symMatrixCreate</a><br>
<a href='# destroy'>-  destroy</a><br>
<a href='# norm'>-  norm</a><br>
<a href='# singular'>-  singular</a><br>
<a href='# newtonIter'>-  newtonIter</a><br>
<a href='# factorDirectLU'>-  factorDirectLU</a><br>
<a href='# solveDirectLU'>-  solveDirectLU</a><br>
<a href='# factorPivotingLU'>-  factorPivotingLU</a><br>
<a href='# solvePivotingLU'>-  solvePivotingLU</a><br>
<a href='# factorCholesky'>-  factorCholesky</a><br>
<a href='# solveCholesky'>-  solveCholesky</a><br>
<a href='# newton'>-  newton</a><br>
</div><br>

		<HR class='big'>
		<P class='sectionTitle'><A name='classinfo'></A>com.wis.math.alg.Decomposition <I>class</I></P>
		<P> <span class='methodTitle'>version:</span> 1.7</P>
		<P class="methodTitle">description:</P>
		<P>Implements the behaviours of the Decomposition Class.
 		        Provides methods for calculating matrix decomposition.
 </P>
		<P class="methodTitle">usage:</P> <pre>var inst:Decomposition = new Decomposition(max);</pre>

<P> <span class='methodTitle'>parameters:</span>
				<ul>
<li>      max  (Number) -- positive integer to clamp maximum newton iterations.</li>
</ul>

			<HR class='small'>
			<P class='groupTitle'><A name='properties'></A>com.wis.math.alg.Decomposition Properties:</P>
			<div class='methodsDiv' >


				<P class='methodTitle'><A name='$order'></A><u> $order</u></P>
				<P> (Number)  -- a positive integer for matrix size.</P>

				<P class='methodTitle'><A name='$element'></A><u> $element</u></P>
				<P> (Array)  -- nested array to hold linear system.</P>

				<P class='methodTitle'><A name='$index'></A><u> $index</u></P>
				<P> (Array)  -- array to hold row-permutation index.</P>

				<P class='methodTitle'><A name='$newtonIter'></A><u> $newtonIter</u></P>
				<P> (Number)  -- integer iteration counter.</P>

				<P class='methodTitle'><A name='$newtonMaxIter'></A><u> $newtonMaxIter</u></P>
				<P> (Number)  -- clamp instantiated in the constructor.</P>

				<P class='methodTitle'><A name='$debug'></A><u> $debug</u></P>
				<P> (String)  -- trace string.</P>
</div>

			<HR class='small'>
			<P class='groupTitle'><A name='methods'></A>com.wis.math.alg.Decomposition Methods:</P>
			<div class='methodsDiv' >


				<P class='methodTitle'><A name=' squareMatrixCreate'></A><u>  squareMatrixCreate</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Square matrix creator.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>inst.squareMatrixCreate(order);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  order   (Number)  -- a positive integer for matrix size.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Void)
    </P>

				<P class='methodTitle'><A name=' symMatrixCreate'></A><u>  symMatrixCreate</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				function description here
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>inst.symMatrixCreate(order);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  order   (Number)  -- a positive integer for matrix size.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Void)
    </P>

				<P class='methodTitle'><A name=' destroy'></A><u>  destroy</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Matrix destructor.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>inst.destroy();</pre>
     </P>
<P><span class='methodAttributesTitle'>returns:</span> (Void)
    </P>

				<P class='methodTitle'><A name=' norm'></A><u>  norm</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Calculates the 1-norm of x.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>inst.norm(x);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  x_arr   (Array)  --</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Number)  --
    </P>

				<P class='methodTitle'><A name=' singular'></A><u>  singular</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				function description here
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>inst.singular();</pre>
     </P>
<P><span class='methodAttributesTitle'>returns:</span> (Boolean)
    </P>

				<P class='methodTitle'><A name=' newtonIter'></A><u>  newtonIter</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Get method to retrieve class property.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>inst.newtonIter;</pre>
     </P>
<P><span class='methodAttributesTitle'>returns:</span> (Number) -- returns instance's total newton method iterations.
    </P>

				<P class='methodTitle'><A name=' factorDirectLU'></A><u>  factorDirectLU</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Attempts to factor the matrix A as A = LU using Gauss
     elimination without row interchanges.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>inst.factorDirectLU();</pre>
     </P>
<P><span class='methodAttributesTitle'>returns:</span> (Boolean)
    </P>

				<P class='methodTitle'><A name=' solveDirectLU'></A><u>  solveDirectLU</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Solves Ax = y after A has been factored as A = LU.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>inst.solveDirectLU(x_arr,y_arr);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  x_arr   (Array)  -- array to hold solution set.</li>
<li>  y_arr   (Array)  -- array for input into solution equation.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Void)
    </P>

				<P class='methodTitle'><A name=' factorPivotingLU'></A><u>  factorPivotingLU</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Attempts to factor a row-permutation of A as PA = LU,
     where P is a row-permutation matrix.  Represent P by
     recording the permutations in the array '$index'.
     Use equilibrated partial pivoting.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>inst.factorPivotingLU();</pre>
     </P>
<P><span class='methodAttributesTitle'>returns:</span> (Boolean)
    </P>

				<P class='methodTitle'><A name=' solvePivotingLU'></A><u>  solvePivotingLU</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Solves Ax = y after A has been factored as PA = LU,
     where P is the row-permutation matrix represented
     by the array '$index'.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>inst.solvePivotingLU(x_arr,y_arr);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  x_arr   (Array)  -- array to hold solution set.</li>
<li>  y_arr   (Array)  -- array for input into solution equation.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Void)
    </P>

				<P class='methodTitle'><A name=' factorCholesky'></A><u>  factorCholesky</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Factors the symmetric positive definite matrix A in the form
     A = LDU, where L is the transpose of U, a unit upper-triangular
     matrix, and where D is a diagonal matrix.  A square root-free
     modification of Cholesky's method is used.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>inst.factorCholesky();</pre>
     </P>
<P><span class='methodAttributesTitle'>returns:</span> (Boolean)
    </P>

				<P class='methodTitle'><A name=' solveCholesky'></A><u>  solveCholesky</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Solves the linear system Ax = y after a has been factored
     by factorCholesky.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>inst.solveCholesky(x_arr,y_arr);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  x_arr   (Array)  -- array to hold solution set.</li>
<li>  y_arr   (Array)  -- array for input into solution equation.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Void)
    </P>

				<P class='methodTitle'><A name=' newton'></A><u>  newton</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Newton's method with damping in n-space.
     <p>
     An attempt to solve f(x) = 0 using Newton's method with damping.
     The Jacobian matrix of f is approximated using finite differences.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>inst.newton(m,f,p_arr,bound);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  m   (Number)  -- positive integer for square matrix order.</li>
<li>  f   (Function)  -- the function.</li>
<li>  p_arr   (Array)  -- array to hold initial vector.</li>
<li>  bound   (Number)  -- error bound.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Array)  -- returns solution set.
    </P>
</div>

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